The time-varying quantum channel model [1]} has been recently proposed with the purpose of including the time fluctuations that are inherent in the decoherence parameters of superconducting qubits [2]}, [3]}, [4]}. In [1]}, several superconducting qubit scenarios were considered depending on the influence of \(T_1\)  and \(T_2\)  on the decoherence effects experienced by these qubits. The time-varying amplitude damping (TVAD) channel was proposed for qubits whose pure dephasing rates are negligible (\(T_1\) -limited) and the time-varying combined amplitude and phase damping channels (TVAPD) were proposed for qubits that have pure dephasing channels that require attention (\(T_1\approx T_2\)  and \(T_2\) -dominated scenarios). In this work we will focus on the asymptotical limits for the TVAD channel.
